(2x+3)x=50

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Solution for (2x+3)x=50 equation: 


Simplifying
(2x + 3) * x = 50

Reorder the terms:
(3 + 2x) * x = 50

Reorder the terms for easier multiplication:
x(3 + 2x) = 50
(3 * x + 2x * x) = 50
(3x + 2x2) = 50

Solving
3x + 2x2 = 50

Solving for variable 'x'.

Reorder the terms:
-50 + 3x + 2x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 3x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-25 + 1.5x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 1.5x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 1.5x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 1.5x + x2 = 0 + 25
1.5x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
1.5x + x2 = 25

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 25 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 25 + 0.5625

Combine like terms: 25 + 0.5625 = 25.5625
0.5625 + 1.5x + x2 = 25.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 25.5625

Calculate the square root of the right side: 5.055937104

Break this problem into two subproblems by setting 
(x + 0.75) equal to 5.055937104 and -5.055937104.


Subproblem 1
x + 0.75 = 5.055937104

Simplifying
x + 0.75 = 5.055937104

Reorder the terms:
0.75 + x = 5.055937104

Solving
0.75 + x = 5.055937104

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 5.055937104 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 5.055937104 + -0.75
x = 5.055937104 + -0.75

Combine like terms: 5.055937104 + -0.75 = 4.305937104
x = 4.305937104

Simplifying
x = 4.305937104


Subproblem 2
x + 0.75 = -5.055937104

Simplifying
x + 0.75 = -5.055937104

Reorder the terms:
0.75 + x = -5.055937104

Solving
0.75 + x = -5.055937104

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -5.055937104 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -5.055937104 + -0.75
x = -5.055937104 + -0.75

Combine like terms: -5.055937104 + -0.75 = -5.805937104
x = -5.805937104

Simplifying
x = -5.805937104


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.305937104, -5.805937104}

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